Ciro Santilli @cirosantilli 37

Types:

Linear combination of a Dirichlet boundary condition and Neumann boundary condition at each point of the boundary.

Examples:

Collection of coordinate charts.

The key element in the definition of a manifold.

Some criticisms:

Every Lie algebra corresponds to a single simply connected Lie group.

The Baker-Campbell-Hausdorff formula basically defines how to map an algebra to the group.

Bibliography:

Techniques to get numerical approximations to numeric mathematical problems.

The entire field comes down to estimating the true values with a known error bound, and creating algorithms that make those error bounds asymptotically smaller.

Not the most beautiful field of pure mathematics, but fundamentally useful since we can't solve almost any useful equation without computers!

The solution visualizations can also provide valuable intuition however.

Important numerical analysis problems include solving:

AGI-complete in general? Obviously. But still, a lot can be done. See e.g.:

Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!

The private key is made of two randomly generated prime numbers: $p$ and $q$. How such large primes are found: how large primes are found for RSA.

The public key is made of:

Given a plaintext message m, the encrypted ciphertext version is:This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.

The inverse operation of finding the private m from the public c, e and $n$ is however believed to be a hard problem without knowing the factors of n.

However, if we know the private p and q, we can solve the problem. As follows.

First we calculate the modular multiplicative inverse. TODO continue.

Bibliography: